Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-12-16
Acta Phys. Polon.41, 2937-2965 (2010)
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, 1 fig.eps. Invited talk at 50-th Cracow School of Theoretical Physics "Particle Physics at the Dawn of the LHC'', Za
Scientific paper
We present a short review describing the use of noncommutative space-time in quantum-deformed dynamical theories: classical and quantum mechanics as well as classical and quantum field theory. We expose the role of Hopf algebras and their realizations (noncommutative modules) as important mathematical tool describing quantum-deformed symmetries: quantum Lie groups and quantum Lie algebras. We consider in some detail the most studied examples of noncommutative space-time geometry: the canonical and $\kappa$-deformed cases. Finally we briefly describe the modifications of Einstein gravity obtained by introduction of noncommutative space-time coordinates.
Lukierski Jerzy
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